For a model[1]} also discuss a more physically self-consistent model which incorporates the finite density in the acceleration region in the form for \(L(E)\) . The corresponding expression for \(L(E)\)  cannot be expressed as a simple closed form and hence is more complicated to use in a best-fit analysis. However, this more correct form nevertheless yields results for \(L_0\)  and \(n\)  that are comparable to those obtained from the “tenuous acceleration region” model used here. in which electrons are accelerated within a region extending from [\(-L_0/2\) ,\(L_0/2\) ] and injected into an external region with uniform density \(n\) , we therefore arrive at the relationship between the observed longitudinal source extent \(L\)  and electron energy \(E\) :
\({L(E) \over 2} = {L_0 \over 2} + \frac{1}{Kn} \, \sqrt{\frac{2}{(\delta - 3)(\delta -5)}} \, E^2.\) 
